KCET 2017

If $\left|\begin{array}{ll}3 & x \\ x & 1\end{array}\right|=\left|\begin{array}{ll}3 & 2 \\ 4 & 1\end{array}\right|$, then $x$ is equal to

If $A=\frac{1}{\pi}\left|\begin{array}{ll}\sin ^{-1}(\pi x) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right|$
$B=\left|\begin{array}{cc}-\cos ^{-1}(\pi x) & \tan ^{-1}\lef...

If $2\left|\begin{array}{ll}1 & 3 \\ 0 & x\end{array}\right|+\left|\begin{array}{ll}y & 0 \\ 1 & 2\end{array}\right|=\left|\begin{array}{ll}5 & 6 \\ 1 & 8\end{array}\right|$, then the value of $x$ and $y$ are

If ${ }^n C_{12}={ }^n C_8$, then $n$ is equal to

The probability distribution of $X$ is
$$ \begin{array}{|c|l|c|c|c|} \hline \boldsymbol{X} & 0 & 1 & 2 & 3 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.3 & k & 2 k & 2 k \\ \hline \end{array} $$
\(\text { The value of } k \text { is }\)

A box has 100 pens of which 10 are defective. The probability that out of a sample of 5 pens drawn one by one with replacement and atmost one is defective, is

Two events $A$ and $B$ will be independent if

The area of triangle with vertices $(K, 0),(4,0)$, $(0,2)$ is 4 sq units, then value of $K$ is

$3+5+7+\ldots$ to $n$ terms is

If $A$ and $B$ are finites sets and $A \subset B$, then

If coefficient of variation is 60 and standard deviation is 24 , then Arithmetic mean is

Equation of line passing through the point $(1,2)$ and perpendicular to the line $y=3 x-1$

Reflexion of the point $(\alpha, \beta, \gamma)$ in $X Y$-plane is

The plane $2 x-3 y+6 z-11=0$ makes an angle $\sin ^{-1}(\alpha)$ with $X$-axis, the value of $\alpha$ is equal to

The perpendicular distance of the point $P(6,7,8)$ from $X Y$-plane is

The distance of the point $(-2,4,-5)$ from the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ is

The value of $\cos ^2 45^{\circ}-\sin ^2 15^{\circ}$ is

If $\mathbf{a}=2 \hat{\mathbf{i}}+\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are orthogonal, then value of $\lambda$ is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are unit vectors such that $a+b+c=0$, then the value of $\mathbf{a} \cdot \mathbf{b}+\mathbf{b} \cdot \mathbf{c}+\mathbf{c} \cdot \mathbf{a}$ is equal to

If $a$ and $\mathbf{b}$ are unit vectors, then angle between $\mathbf{a}$ and $\mathbf{b}$ for $\sqrt{3} \mathbf{a}-\mathbf{b}$ to be unit vector is

The output of a step down transformers is measured to be 48 V when connected to a 12 W bulb. The value of peak current is

A coil of inductive reactance $1 / \sqrt{3} \Omega$ and resistance $1 \Omega$ is connected to a $200 \mathrm{~V}, 50 \mathrm{~Hz}$ AC supply. The time lag between maximum voltage and current is

In the A.C. circuit shown, keeping ' $K$ ' pressed, if an iron rod inserted into the coil, the bulb in the circuit,

The scientist who is credited with the discovery of 'nucleus' in an atom is

The mass defect of ${ }_2^4 \mathrm{He}$ is 0.03 u . The binding energy per nucleon of helium (in MeV) is

The energy (in eV ) required to excite an electron from $n=2$ to $n=4$ state in hydrogen atom is

In a nuclear reactor, the function of the moderator is to decreases

The particle emitted in the decay of ${ }_{92}^{238} \mathrm{U}$ to ${ }_{92}^{234} \mathrm{U}$

The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances $1 \mathrm{pF}, 2 \mathrm{pF}$ and 4 pF

A system of two capacitors of capacitance $2 \mu \mathrm{~F}$ and $4 \mu \mathrm{~F}$ is connected in series across a potential difference of 6 V . The electric charge and energy stored in a system are

Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls when in air

The angle between velocity and acceleration of a particle describing uniform circular motion is

A basic communication system consists of
(i) Transmitter
(ii) Information sources
(iii) User of information
(iv) Channel
(v) Receiver

A piece of copper is to be shaped into a conducting wire of maximum resistance. The suitable length and diameter are ......................and............................respectively.

A cylindrical conductor of diameter 0.1 mm carries a current of 90 mA . The current density ( in $\mathrm{Am}^{-2}$ ) is ( $\pi \approx 3$ )

In meter bridge experiment, with a standard resistance in the right gap and a resistance coil dipped in water (in a beaker) in the left gap, the balancing length obtained is ' $l$ '. If the temperature of water is increased, the new balanci...

The power dissipated in $3 \Omega$ resistance in the following circuit is

\(\text { The value of } I \text { in the figure shown below is }\)

Of the following graphs, the one that correctly represents the $I-V$ characteristics of a 'Ohmic device' is

A galvanometer of resistance $50 \Omega$ is connected to a battery of $3 \cdot \mathrm{~V}$ along with a${ }^{\text { }}$ resistance of $2950 \Omega$ in series shows full-scale deflection of 30 divisions. The additional series resistance re...

A particle is dropped from a height $H$. The de-Broglie wavelength of the particle depends on height as

From the following graph of photo current against collector plate potential, for two different intensities of light $I_1$ and $I_2$, one can conclude

'Young's modulus' is defined as the ratio of

A jet plane of wing span 20 m is travelling towards west at a speed of $400 \mathrm{~ms}^{-1}$. If the earth's total magnetic field is $4 \times 10^{-4} \mathrm{~T}$ and the dip angle is $30^{\circ}$, at that place, then the voltage differe...

The working of magnetic braking of trains is based on

A bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a net acceleration, is

If $\mathbf{E}$ and $\mathbf{B}$ represent electric and magnetic field vectors of an electromagentic wave, the direction of propagation of the wave is along

Two point charges $A=+3 \mathrm{nC}$ and $B=+1 \mathrm{nC}$ are placed 5 cm apart in air. The work done to move charge $B$ towards $A$ by 1 cm is

Two spheres of electric charges +2 nC and -8 nC are placed at a distance $d$ apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?

$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of the electric field (in $\mathrm{NC}^{-1}$ ) at a distance of 20 cm from its centre is